Value a stream of payments that never ends: a level perpetuity, a growing perpetuity, a perpetuity due or one that starts later. Solve for the present value, the payment or the discount rate, and see how much of the value comes from the first decades.
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Solve for
Perpetuity details
$
Cash received each period, starting with this amount.
$
%
Required return. Divided by payments per year.
%
0 for a level perpetuity. Must be below the discount rate.
1 = end of first period (ordinary), 0 = today (due), 5 = deferred.
Enter your values to see the result.
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How to use the Perpetuity Calculator
Choose what to solve for: present value, the payment, or the discount rate.
Enter the first payment and, if solving for the payment or rate, the present value or price.
Enter the annual discount rate and growth rate. Use 0% growth for a level perpetuity.
Pick the payment frequency and timing: 1 for an ordinary perpetuity, 0 if the first payment is today, or a later period for a deferred one.
Read the result and working, then check the horizon table to see how much value comes from distant payments.
Perpetuity formulas
A perpetuity is a series of payments that continues forever. Because each payment further out is discounted more heavily, the infinite sum still has a finite value as long as the discount rate is above the growth rate.
Type
Present value
Example (C = 1,000, r = 8%, g = 3%)
Level perpetuity (first payment in 1 period)
PV = C ÷ r
1,000 ÷ 0.08 = 12,500
Growing perpetuity
PV = C ÷ (r − g)
1,000 ÷ 0.05 = 20,000
Perpetuity due (first payment today)
PV = C ÷ (r − g) × (1 + r)
20,000 × 1.08 = 21,600
Deferred (first payment in period k)
PV = C ÷ (r − g) ÷ (1 + r)k − 1
k = 6: 20,000 ÷ 1.085 = 13,611.66
Payment from a value
C = PV × (r − g)
20,000 × 0.05 = 1,000
Discount rate from a price
r = C ÷ PV + g
1,000 ÷ 20,000 + 0.03 = 8%
r and g are rates per payment period. With quarterly payments at an 8% annual rate, r = 2% per quarter and C is the quarterly payment.
Value multiple: present value per 1 of first payment
The table shows 1 ÷ (r − g), how many times the first annual payment a perpetuity is worth. Notice how fast the multiple rises as growth approaches the discount rate.
Discount rate
g = 0%
g = 2%
g = 3%
g = 4%
5%
20.0×
33.3×
50.0×
100.0×
6%
16.7×
25.0×
33.3×
50.0×
8%
12.5×
16.7×
20.0×
25.0×
10%
10.0×
12.5×
14.3×
16.7×
12%
8.3×
10.0×
11.1×
12.5×
Tips for using perpetuity values
Watch the r − g gap. A one-point change in growth or discount rate can change a growing perpetuity's value by 20-50%. Test a range of assumptions instead of relying on a single number.
Keep growth realistic. For terminal values, long-run growth is usually set near expected inflation or long-term economic growth, not a company's recent growth rate.
Match payment and rate timing. C ÷ r assumes the first payment comes one full period from now. If you are paid today, use the perpetuity due version.
Use nominal or real consistently. Discount nominal payments with a nominal rate, or inflation-adjusted payments with a real rate.
Frequently asked questions
What is the formula for the present value of a perpetuity?
For a level perpetuity whose first payment arrives one period from now, PV = C ÷ r, where C is the payment per period and r the discount rate per period. A perpetuity paying 1,000 a year discounted at 8% is worth 1,000 ÷ 0.08 = 12,500.
How do you value a growing perpetuity?
Use PV = C ÷ (r − g), where C is the first payment (received one period from now), r the discount rate and g the constant growth rate per period. With C = 1,000, r = 8% and g = 3%, PV = 1,000 ÷ 0.05 = 20,000. This is the same formula as the Gordon growth model for stocks and the terminal value in a DCF.
Why must the discount rate be higher than the growth rate?
If payments grow as fast as or faster than the rate used to discount them, each future payment is worth at least as much today as the one before, so the sum never stops growing and the value is infinite. The formula C ÷ (r − g) only works when r is greater than g.
What is a perpetuity due?
A perpetuity due pays its first amount immediately instead of one period from now. Its value is the ordinary value multiplied by (1 + r), or equivalently C + C ÷ r for a level perpetuity. Enter 0 as the first payment period to calculate it.
How do I value a perpetuity that starts in the future?
Value it one period before its first payment with C ÷ (r − g), then discount that amount back to today: PV = C ÷ (r − g) ÷ (1 + r)^(k − 1), where k is the period of the first payment. Enter that period in the calculator to get a deferred perpetuity.
Are perpetuities real?
A few instruments come close: some preferred stocks pay a fixed dividend with no maturity, a handful of perpetual government and corporate bonds exist, and endowments aim to fund spending forever. The perpetuity formula is also widely used for terminal values in company valuations and for land or rental valuation.
How much of a perpetuity's value comes from distant payments?
Less than you might think. At an 8% discount rate with no growth, payments in the first 30 years make up about 90% of the value. Higher growth pushes more value into the distant future, which is why growing perpetuities are very sensitive to the r − g gap.
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